Farid told me to clarify the comment I made about the first narration so here I go.
Different recitations can come in two forms:
A- That which agrees with the written text inside the `Uthmani Mushaf.
B- That which differs from the written text inside the `Uthmani Mushaf. This one is split into two subsections: 1-What differs very slightly (such as the addition of a single letter or its subtraction or substitution by another or the flipping of two words in the structure of a sentence like saying "Great and wise" instead of "Wise and great") 2-What differs greatly (such as the addition/subtraction of a word or its substitution by another word). This last one can be split into two categories: 1-A change that can be reconciled with the meaning of the verse as we know it. 2-A change that cannot be reconciled and changes the meaning altogether.
Now the question is, WHY does this happen?
Here is why based on my limited research, regardless of what case we are talking about from those listed above:
1- The verses would usually be revealed separately and not in the order we find in our complete Masaahif today. At the end of each year, Jibreel (as) would descend and recite to the Prophet (saw) whatever was revealed from the Qur'an up until that specific year, by doing so the scattered verses would be joined and placed in their final Qur'anic order and this could slightly alter the structure of a verse as is clear. Due to this, when one reviews the narrations he'd notice that the Companions place a lot of importance on keeping up with the newest recitations. However, some Companions may miss some of these or may not be up to date and they'd read a verse in its older form and think that their recitation is the mainstream adopted one.
2- The Naskh or abrogation of the verses was also taking place, this is to cater to the ever changing situation and evolution of Muslim society. Therefore, one ruling replaces another, meaning that one verse would replace another one and annul its ruling or update it. Moreover, verses would be revealed (maybe in the form of Hadith-Qudsi) but they will not be included in the final text of the Qur'an, similar to the verses of stoning and how the Prophet (saw) never permitted `Umar to write it down as part of the Mushaf, this is an abrogated verse. Scholars have preserved for us a lot of the texts of such abrogated verses or Ahadith Qudsiyyah only for the benefit and for us to have more information and a more complete picture. A few Companions may not realize that a verse was abrogated for various reasons, they would carry-on reciting it while thinking it is still Qur'an.
3- The seven letters/Ahruf of the Arabs, this was a system by which Allah would make things easy for us and allow the various Arabs in the region whether Yemenis or Shamis or Masris or `Iraqis or Hijazis or Bahraynis to recite various words differently based on their understanding of them, two different tribes may express the same meaning differently, they may have different words for the same general purpose, whether substituting one word for another or slightly changing the structure of a sentence. Later in the time of `Uthman, the newer generations of Muslims and new converts never grasped this idea, so they began to fight, this is why `Uthman decided to unify them on one written text and burn the rest, he did not though limit them to one recitation and various ways of reciting continued but sooner or later most were dismissed if they opposed the `Uthmani text. The Qur'an we have in our hands today has a mixture of these seven letters but evidence suggests that it is mostly by the tongue of Quraysh.
4- Mis-attribution to the the Companion/Sahabi, a lot of the narrations that mention these different recitations are weak and very unreliable, even those with authentic chains may have hidden defects. Therefore, it is due to common sense and logic that we avoid relying on these texts if they oppose what is Mutawatir through hundreds of people. This is mostly noticeable when one of these odd reports attributed to a certain Companion conflicts with a popular recitation by that same Companion. In other words, sometimes a single odd report will claim that Ibn Mas`oud recited a verse in an unfamiliar way, on the other hand we have with us today authentic Mutawatir chains leading up to Ibn mas`oud in which he recites it as we all know it. So the mistakes by the narrators are a factor.
5- The mistakes of the Companions also play a role, while points 1 & 2 briefly touch on this subject, yet we know for a fact that the nature of humanity makes falling into error a very common and natural matter. Due to old age, forgetfulness, or simply mishearing certain words, and because the Qur'an was a very large book for its time, we never at any point expect every man to gather the entire book flawlessly without imperfections, so even the biggest of Companions may err here or there and the hand of Allah is with the majority and it isn't possible that the entire nation and all those great scholars from the Companions are wrong while two or three individuals are correct. So if Ibn `Abbas recites a verse differently than the Qur'an that was officially adopted by Abu Bakr, `Umar, `Uthman and `Ali in the presence of all major Companions and Huffadh such as Mu`adh Ibn Jabal and Salim Mawla Hudhayfah, we simply dismiss Ibn `Abbas's recitation if it differs with the Jamaa`ah.
My research led me to the above points, there may as well be others but that requires more reading.